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On the Hardness of the Lee Syndrome Decoding Problem

27 February 2020
Violetta Weger
Karan Khathuria
Anna-Lena Horlemann
Massimo Battaglioni
Paolo Santini
Edoardo Persichetti
ArXiv (abs)PDFHTML
Abstract

In this paper we study the hardness of the syndrome decoding problem over finite rings endowed with the Lee metric. We first prove that the decisional version of the problem is NP-complete, by a reduction from the 333-dimensional matching problem. Then, we study the complexity of solving the problem, by translating the best known solvers in the Hamming metric over finite fields to the Lee metric over finite rings, as well as proposing some novel solutions. For the analyzed algorithms, we assess the computational complexity in the asymptotic regime and compare it to the corresponding algorithms in the Hamming metric.

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